Image-forming MR methods, which utilize the interaction between magnetic field and nuclear spins in order to form two-dimensional or three-dimensional images are widely used nowadays, notably in the field of medical diagnostics, because for the imaging of soft tissue they are superior to other imaging methods in many respects, they do not require ionizing radiation, and they are usually not invasive.
According to the MR method in general, the body of a patient or in general an object to be examined is arranged in a strong, uniform magnetic field BO whose direction at the same time defines an axis, normally the z-axis, of the coordinate system on which the measurement is based.
The magnetic field produces different energy levels for the individual nuclear spins in dependence on the applied magnetic field strength which spins can be excited (spin resonance) by application of an alternating electromagnetic field (RF field) of defined frequency, the so called Larmor frequency or MR frequency. From a macroscopic point of view the distribution of the individual nuclear spins produces an overall magnetization which can be deflected out of the state of equilibrium by application of an electromagnetic pulse of appropriate frequency (RF pulse) with an effective magnetic field perpendicular to the z-axis, so that the magnetization performs will process about the z-axis.
Any variation of the transverse magnetization can be detected by means of receiving RF antennas, which are arranged and oriented within an examination volume of the MR device in such a manner that the variation of the magnetization is measured in the direction perpendicularly to the z-axis.
In order to realize spatial resolution in the body, switching magnetic field gradients extending along the three main axes are superposed on the uniform magnetic field, leading to a linear spatial dependency of the spin resonance frequency. The signal picked up in the receiving antennas then contains components of different frequencies which can be associated with different locations in the body.
The signal data obtained via the receiving antennas corresponds to the spatial frequency domain and is called k-space data. The k-space data usually includes multiple lines acquired with different phase encoding, resulting from different RF excitations. Each line is digitized by collecting a number of samples. A set of samples of k-space data is converted to an MR image, e.g. by means of the Fast Fourier Transform.
This approach theoretically permits to obtain MR images at high quality when the MR samples are acquired on a perfect rectilinear grid. However, since MRI relies on spatial encoding of magnetic field gradients, any kinds of imperfections in the gradient fields as well as any kinds of imperfections in the main magnetic field lead to deviation of samples from the rectilinear grid, and a variety of MR image defects, including for example image distortions, ghosting, blurring and shifts within the MR images.
Distortions in the main magnetic field may occur for example due to inherent magnetic field imperfections resulting from non-perfect manufacturing of magnets, magnet drifts, heating effects, Eddy current effects etc. Additionally, limited fidelity and bandwidth of gradient amplifiers, coupling among gradient coils and self-induction in gradient coils leads to field perturbations of the magnetic gradient fields which are thus sometimes far from being perfect.
Characterization of the magnetic field using magnetic field monitoring (MFM) probes is known from literature, e.g. from Magn. Res. Med. 60:187-197 (2008) and Magn. Res. Med. 60:176-186 (2008). Magn. Res. Med. 60:187-197 (2008) discusses a method to derive spatiotemporal magnetic field components from data obtained with multiple receive probes placed around the object of interest, inside the magnetic field. It is based on the model assumption that phase variations as observed by the probes results from variations in the magnetic field. However, other sources of phase variations may also be present, like patient physiology induced load variations of the body transmit RF coil.
In its initial form, the MFM probes were receive-only probes, which came with several limitations as discussed in Magn. Res. Med. 62:269-276 (2009). Further, in this paper it was proposed to modify the probes to Transmit-Receive probes, for which the monitored signal phase indeed will reflect the magnetic field induced phase, and be less susceptible to the RF disturbances from the presence of a patient.